Portfolio optimization under nonlinear utility

Gregor Heyne, Michael Kupper, Ludovic Tangpi

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

This paper studies the utility maximization problem of an agent with nontrivial endowment, and whose preferences are modeled by the maximal subsolution of a backward stochastic differential equation (BSDE). We prove existence of an optimal trading strategy and relate our existence result to the existence of a maximal subsolution to a controlled decoupled forward-BSDE (FBSDE). Using BSDE duality, we show that the utility maximization problem can be seen as a robust control problem admitting a saddle point if the generator of the BSDE additionally satisfies a specific growth condition. We show by convex duality that any saddle point of the robust control problem agrees with a primal and a dual optimizer of the utility maximization problem, and can be characterized in terms of a BSDE solution.

Original languageEnglish (US)
Article number1650029
JournalInternational Journal of Theoretical and Applied Finance
Volume19
Issue number5
DOIs
StatePublished - Aug 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Finance
  • Economics, Econometrics and Finance(all)

Keywords

  • Subsolutions of BSDEs
  • convex duality
  • submartingale
  • utility maximization

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